In the previous Tip, , we showed how to state the Null Hypothesis as an equation (e.g. H0: μΑ = μΒ).
And the Alternative Hypothesis would be the opposite of that (HA: μA ≠ μB).
These would work for a 2-tailed (2-sided) tests, when we only want to know whether there is a (Statistically Significant) difference between the two Means, not which one may be bigger than the other.
But what about when we do care about the direction of the difference? This would be a 1-tailed (1-sided) test. And the Alternative Hypothesis will tell us whether it's right-tailed or left-tailed. (We need to specify the tail for our statistical calculator or software.)
How does this work? First of all, it's helpful to know that the Alternative Hypothesis is also known as the "Maintained Hypothesis". The Alternative Hypothesis is the Hypothesis which we are maintaining and would like to prove.
We maintain that the Mean lifetime of the lightbulbs we manufacture is more than 1,300 hours. That is, we maintain that µ > 1,300.
This, then becomes our Alternative Hypothesis. HA: µ > 1,300
Note that the comparison symbol of HA points to the right. So, this test is right-tailed.
If, on the other hand, we maintained that the Mean defect rate of a new process is less than the Mean defect rate of the old process, our Maintained/ Alternative Hypothesis would be HA: µ New < µ Old
and the test would be left-tailed.
Andrew A. (Andy) Jawlik is the author of the book, Statistics from A to Z -- Confusing Concepts Clarified, published by Wiley.